Finite Group Databasebeta

C2×#20299720 #28407826

order14464
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productC2×#20299720

Splittings

SylowC113 ⋊ C2×#504

Subgroups

subgroupG/H
centerC22C22×#11744762
commutatorC2×C113C23×C8
FrattiniC2C23×#11744762
FittingC2×Q8×C113C8
socleC22×C113C22×C8
prime radicalC2×#14268648C4
cosocle#11744753C24
hypercenterC2×Q8#11744762
hypocenterC113C2×#504
LCSG ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C2×Q8

368 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7232

Conjugacy classes & character table

220 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 21762);